1. **State the problem:** We have two intersecting lines forming four angles around the intersection point. One angle, $\angle y$, is given as 99°. We need to find the measures of angles $x$, $y$, and $z$. 2. **Recall the rule:** When two lines intersect, opposite (vertical) angles are equal, and adjacent angles are supplementary (sum to 180°). 3. **Given:** $\angle y = 99^\circ$. 4. **Find $\angle x$:** Since $x$ and $y$ are vertical angles, they are equal. $$\angle x = \angle y = 99^\circ$$ 5. **Find $\angle z$:** $z$ is adjacent to $y$, so they are supplementary. $$\angle z + \angle y = 180^\circ$$ $$\angle z + 99^\circ = 180^\circ$$ $$\angle z = 180^\circ - 99^\circ = 81^\circ$$ 6. **Summary:** - $\angle x = 99^\circ$ - $\angle y = 99^\circ$ - $\angle z = 81^\circ$